[seqfan] Simple Puzzler

David Wilson davidwwilson at comcast.net
Mon Feb 7 01:51:28 CET 2011

Divide your paper into 3 sections. In one section write the number 2, in a different section write the number 3. Thereafter, if two numbers are in distinct sections, write their product in the third section. For example, 6 = 2*3 goes into the initially empty section, then 12 = 2*6 goes into the same section with 3, etc.

1. Does the same number ever end up in two distinct sections?

2. Obviously all numbers will be of the form 2^k * 3^j with j,k >= 0. Which of these numbers never appear?

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